Torsion-free connections with prescribed curvature

Advances in Geometry 2026 Open access

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Authors: Efrain Basurto-Arzate
DOI: 10.1515/advgeom-2026-0011
Cited by: 0
References: 15

Abstract

Abstract We provide necessary and sufficient conditions for a map S : U → K (𝔤) to arise from the curvature tensor of a torsion-free connection on a sufficiently small neighborhood by using a suitable power series approach. This torsion-free connection is uniquely given. The curvature map S is used to effectively compute the holonomy of this connection.

Fields of Study & Subjects

Mathematics and Applications

Publication details

Journal / source
Advances in Geometry
Publisher
Walter de Gruyter GmbH
Volume
26
Issue
3
Pages
387–406
Publication date
1 July 2026
Language
EN